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PHYS-222 Worksheet 9 for Section 25 & 36 TA: Yang Li, [email protected] October 7, 2012 Problem 9-1 ~ r) in the following cases: Use Ampere’s law to calculate the magnetic field B(~ a. a long straight wire carries electric current I (the transverse diameter of the wire can be neglected); 0I key: B = µ2πr b. two long wires both carry electric current I in the same direction. The separation distance between µ0 I µ0 I two wires is d (the transverse diameter of the wire can be neglected); key: B = 2π(d/2+r) + 2π(d/2−r) c. a long cylindrical wire carries uniform electric current I. The radius of the wire is a. Calculate magnetic µ0 Ir 0I field both inside and ourside the wire; key: B = µ2πr (r > a), B = 2πa (r ≤ 0) 2 d. a long cylindrical solenoid carries electric current I. The length of the solenoid is L and the number of coils is N . The radius of the solenoid is a; Find the magnetic field both inside and outside the solenoid. key: B = N (r ≤ a), B = 0 (r > a) L µ0 I e. a very large conducting sheet carries uniform electric current. The current per unit length is σ. key: B = µ20 σ Problem 9-2 A current I flows in a plane rectangular current loop with height w and horizontal sides b. The loop is placed ~ in such a way that the sides of length w are perpendicular to B ~ (Figure (a)) into a uniform magnetic field B ~ (Figure (b)) . Calculate τ , the magnitude of , and there is an angle θ between the sides of length b and B the torque about the vertical axis of the current loop due to the interaction of the current through the loop with the magnetic field. key: τ = BIwb sin θ (a) (b) 1